91Ó°ÊÓ

$v_B=v$

$v_B^{\text{'}}=v/2$

Let, ball B be moving in a positive direction with speed v and ball A be at the origin. But after collision, the direction of ball B will be in negative y– axis with half speed. At the same time, the speed of ball A may reduce to half. As ball A is stationary and both the balls contain different masses, logically, ball A will move inthedirection along x-positive axis. Here, linear momentum is conserved.According to conservation of linear momentum, momentum that characterizes motion never changes in an isolated collection of objects.

Formula is as follow:

Initial momentum = Final momentum

Conservation of linear momentum along x and y axis can be given as,

$$\begin{gathered} m_B{v}_B=m_B{v}_B^{\text{'}}\cos \mathrm{θ}+m_A{v}_A^{\text{'}}\cos \mathrm{ϕ}......\left(1\right) \\ 0=m_B{v}_B^{\text{'}}\sin \mathrm{θ}+m_A{v}_A^{\text{'}}\sin \mathrm{ϕ}......\left(2\right) \end{gathered}$$

where, $m_B$ denotes mass of ballB

$v_B$ denotes velocity of ball B,

$V_b^{\text{'}}$ denotes velocity of ball B after collision,

$m_A$ denotes mass of ball A,

$v_A$ denotes velocity of ball A,

$v_A^{\text{'}}$ denotes velocity of ball A after collision.

Now, to find the direction of ball A after collision, only consider A part from equation (2). Therefore,

$$\begin{gathered} 0=m_B{v}_B^{\text{'}}\sin \mathrm{θ}+m_A{v}_A^{\text{'}}\sin \mathrm{ϕ} \\ {m}_A{v}_A^{\text{'}}\sin \mathrm{ϕ}=m_B\frac{v}{2}.....\left(3\right) \end{gathered}$$

Also, for x- direction, equation (1) will be,

$$\begin{gathered} m_B{v}_B=m_B{v}_B^{\text{'}}\cos \mathrm{θ}+m_A{v}_A^{\text{'}}\cos \mathrm{ϕ} \\ {m}_A{v}_A^{\text{'}}\cos \mathrm{ϕ}=m_B{v}_B.....\left(4\right) \end{gathered}$$

Dividing equations (3) and (4), therefore,

$$\begin{gathered} \tan \mathrm{ϕ}=1/2 \\ \mathrm{ϕ}=27° \end{gathered}$$

Thus, ball A moves at an angle of $27°$.

To find the velocity of ball Aafter collision, from equation (1) or (2), values for masses of ball A and B are needed. Since, these values are not given, the speed of ball A cannot bedetermined.

Hence,it is shown that speed of A cannot be determined fromthegiven information.

Therefore, using the law of conservation of linear momentum, the direction of motion of the ball after the collision can be determined.